A. Field of the Invention
The present invention relates generally to photonic bandgap materials (also known as photonic crystals), and, more particularly to hetero-structure photonic bandgap materials.
B. Description of the Related Art
During the last decade photonic crystals have risen from an obscure technology to a prominent field of research. In large part this is due to their unique ability to control, or redirect, the propagation of light. E. Yablonovich, xe2x80x9cInhibited spontaneous emission in solid-state physics and electronics,xe2x80x9d Physical Review Letters, vol. 58, pp. 2059-2062 (May 1987), and S. John, xe2x80x9cStrong localization of photons in certain disordered dielectric superlattices,xe2x80x9d Physical Review Letters, vol. 58, pp. 2486-2489 (June 1987), initially proposed the idea that a periodic dielectric structure can possess the property of a bandgap for certain frequencies in the electromagnetic spectra, in much the same way as an electronic bandgap exists in semiconductor materials. This property affords photonic crystals with a unique ability to guide and filter light as it propagates within it. Thus, photonic crystals have been used to improve the overall performance of many optoelectronic devices.
The concept of a photonic bandgap material is as follows. In direct conceptual analogy to an electronic bandgap in a semiconductor material, which excludes electrical carriers having stationary energy states within the bandgap, a photonic bandgap in a dielectric medium excludes stationary photonic energy states (i.e., electromagnetic radiation having some discrete wavelength or range of wavelengths) within that bandgap. In semiconductors, the electronic bandgap results as a consequence of having a periodic atomic structure upon which the quantum mechanical behavior of the electrons in the material must attain eigenstates. By analogy, the photonic bandgap results if one has a periodic structure of a dielectric material where the periodicity is of a distance suitable to interact periodically with electromagnetic waves of some characteristic wavelength that may appear in or be impressed upon the material, so as to attain quantum mechanical eigenstates.
A use of these materials that can be envisioned, is the optical analog to semiconductor behavior, in which a photonic bandgap material, or a plurality of such materials acting in concert, can be made to interact with and control light wave propagation in a manner analogous to the way that semiconductor materials can be made to interact with and control the flow of electrically charged particles, i.e., electricity, in both analog and digital applications. Photonic crystals have been used to improve the overall performance of many optoelectronic devices.
Optimizing the performance of a Photonic Integrated Circuit (PIC) in a single crystalline photonic crystal structure (unistructure) continues to be a challenge, due to the spatial constraint of the unistructure. This limitation, namely single crystalline structures, has a pronounced impact over the bandgap size, throughput efficiency, and back reflections that arise due to spatial mismatches at transitions between different Photonic crystal sections such as straight and angular waveguides.
Conventional two-dimensional photonic crystals have been formed from an evenly-spaced triangular lattice array of rods, each rod having a dielectric constant, and a background material surrounding the rods and having a dielectric constant different than the dielectric constant of the rods. Such a triangular lattice array photonic crystal is shown, for example, in FIG. 2 of U.S. Pat. No. 5,999,308. As shown in this patent, the triangular array consists of rows of rods, wherein adjacent rows of rods are offset from each other such that a rod from one row lies between two rods on an adjacent row in the z-direction.
The method initially used for theoretical analyses of photonic crystal structures is the plane-wave expansion method, which makes use of the fact that; eigenmodes in periodic structures can be expressed as a superposition of a set of plane waves. Using this approach, photon dispersion relations inside photonic crystal structures have been calculated. While this method can ensure an accurate solution for the dispersion properties of a photonic crystal structure, it is still limited due to the fact that transmission spectra, field distribution, and back reflections cannot be extracted, since it only considers propagating modes, whereas in a finite crystal there are also evanescent modes.
An alternative approach, which has been widely adopted in calculating both transmission spectra and field distribution, is based on numerical solutions of Maxwell equations using the finite-difference time-domain (FDTD) method. In particular, FDTD has been used to analyze multi-channel drop/add filters as well as other photonic crystal devices, to calculate transmission through sharp bends, and to study waveguiding mechanism through localized coupled cavities in three-dimensional photonic crystals.
To examine the FDTD method, a two-dimensional photonic crystal of a square lattice with a lattice constant xcex1=543 nm may be considered. The lattice may include dielectric rods with a dielectric constant of ∈r=11.56 and radius r=109 nm, in an air background. The transmission spectrum for this structure may be obtained using FDTD with periodic boundary conditions. The structure has a bandgap between xcex=1.234 xcexcm and xcex=2.172 xcexcm, for TM (transverse magnetic field) polarization. A beam splitter may be implemented in the structure to calculate its overall throughput efficiency.
A common use for photonic crystals in integrated optical applications is that of an optical beam splitter and/or combiner. An optical beam splitter divides an optical beam into multiple signals for density routing. The split beam can then be recombined back into a single beam or further guided to another point with an optical beam combiner, depending upon the application. Presently, these operations have been hindered by the spatial constraints of the single crystalline structure, which in some cases limit their ability to efficiently perform their intended functions. Limitations such as back reflections, frequency selectivity, and/or bi-directionality of certain devices may have a pronounced impact on the performance and operation of some photonic integrated circuits. The hetero-structure photonic crystal devices of the present invention overcome these limitations, in addition to enhancing throughput efficiency as well as minimizing back reflections.
A conventional two-dimensional photonic crystal is the Cartesian lattice array 10 shown in FIG. 1. The Cartesian lattice array 10 may be a square array or rectangular array and is formed from evenly-spaced columns and rows of rods 12, each rod 12 having a dielectric constant, and background material 14 surrounding rods 12 and having a dielectric constant different than the dielectric constant of rods 12. As shown in FIG. 1, the Cartesian lattice array 10 consists of rows and columns of rods 12, wherein adjacent rows and columns of rods 12 are evenly spaced from each other in both the x-direction and the z-direction. As will be described more fully below, a line defect may be formed in Cartesian lattice array photonic crystal 10 by removing a portion of a column of dielectric rods 12 from the photonic crystal 12. This creates a main waveguide 16 within the photonic crystal 10.
The unistructure optical beam splitter 10 shown in FIG. 1 consists of silicon posts 12 (having a dielectric constant ∈r=11.56) arranged on a rectangular lattice in air background 14 (having a dielectric constant ∈b=1.0). The photonic crystal structure 10 possesses a bandgap between xcex=1.234 xcexcm and xcex=2.172 xcexcm for TM polarization. An optical beam splitter (Y coupler) 10 consists of two basic elements, a waveguiding element 16 and wavesplitting elements 18, 20. Creating a straight-line defect in a photonic crystal forms the waveguiding element 16, while creating an angular line defect forms the wavesplitting elements 18, 20. Such that each wavesplitting element makes 45xc2x0 from the main waveguiding element 16 as shown in FIG. 1. Line defects can be created by either adding or removing high-index material, altering the effective index of the waveguide in comparison to its surroundings. In the structure 10 of FIG. 1 a row of dielectric posts was removed to create an acceptor type waveguide. Adding high-index material to the waveguiding region creates donor type waveguides.
An incident plane wave of normal incidence with a frequency profile within the bandgap of the photonic crystal structure may be used to excite the input waveguide 16 of the Y coupler 10. A detector may be placed inside each waveguide channel 18, 20 of the splitter 10, the time varying electric field measured, and then compared to the incident field in the main channel (input) 16, to calculate the throughput efficiency. The structure shown in FIG. 1 was simulated using two-dimensional FDTD along with Perfectly Matched Layer (PML) absorbing boundary conditions to truncate the computational region and minimize the reflections from the outer boundary. A pulse of center wavelength xcex=1.55 xcexcm and pulse width xcex94xcex=0.5 xcexcm incident through the main waveguiding element 16 should ideally split with 50% transmission efficiency on either side of the splitting element. Comparing the amplitude of the time varying electric field stored at the detectors placed inside each waveguide channel 18, 20 of the splitter 10, with the amplitude of the incident field through the main waveguide channel 16, the transmission efficiency in each channel 18, 20 was numerically calculated to be about 25% for frequencies within the bandgap of the structure, and the overall throughput efficiency was 50% through both channels. The same holds true for the unistructure (triangular lattice array photonic crystal) shown in FIG. 2 of U.S. Pat. No. 5,999,308.
A considerable amount of loss was numerically measured (3 dB), which is mainly due to back reflections at the transition between the waveguiding section 16 and the wavesplitting sections 18, 20, as well as bending losses at the corner joints between the angular and straight waveguide sections. Such losses caused a mismatch between the waveguiding section 16 and the wavesplitting sections 18, 20, and hence reduced the overall throughput efficiency of the unistructure beam splitter. In other words, due to geometrical limitations of the rectangular grid 12 on which the rectangular photonic crystal lattice was formed, unistructure beam splitter 10 did not achieve its predicted performance. Even though other approaches were successfully capable of achieving better performance than the device 10 analyzed above, they still suffered from other issues such as waveguide directivity, that is, being a bi-directional waveguide instead of a unidirectional one. In addition, other approaches use a frequency selective waveguide instead of a broadband one, using localized point defects to enhance the overall throughput efficiency of such devices. Such techniques are better utilized for narrowband or selectively coupled devices, while their performance for broadband devices may not be optimal.
Thus there is a need in the art to provide a photonic crystal lattice arrangement that increases the transmission efficiency of light through the crystal above the transmission efficiencies encountered with the conventional unistrucuture lattices described above.
The present invention satisfies this need by providing a two-dimensional, hetero-structure photonic crystal that includes a hybrid combination of rectangular and triangular lattice arrays of dielectric rods.
The two-dimensional, hetero-structure photonic crystal of the present invention provides the advantages of both the rectangular and triangular lattice arrays for application with optical beam splitters (also known as Y couplers) and combiners. The two-dimensional, hetero-structure photonic crystal of the present invention achieved a transmission efficiency greater than 90% in comparison to the transmission efficiency of 50% for the conventional uni-structure photonic crystals.
Additional advantages of the invention will be set forth in part in the description which follows, and in part will be learned from the description, or may be learned by practice of the invention. The advantages of the invention will be realized and attained by means of the elements and combinations particularly pointed out in the appended claims.
In accordance with the purpose of the invention, as embodied and broadly described herein, the invention comprises a two-dimensional, hetero-structure photonic crystal, comprising: a rectangular lattice array of dielectric rods provided on a portion of an air background; and a triangular lattice array of dielectric rods provided adjacent to said rectangular lattice array, wherein a main waveguide is formed in said rectangular lattice array by removing dielectric rods from portions thereof, and a plurality of splitting channel waveguides are formed in said triangular lattice array by removing dielectric rods from portions thereof, each of the plurality of splitting channel waveguides optically communicating with the main waveguide.
Further in accordance with the purpose, the invention comprises A method of making a two-dimensional, hetero-structure photonic crystal, comprising: forming a rectangular lattice array of dielectric rods on a portion of an air background; forming a triangular lattice array of dielectric rods provided adjacent to said rectangular lattice array; forming a main waveguide in the rectangular lattice array by removing dielectric rods from portions thereof; and forming a plurality of splitting channel waveguides in the triangular lattice array by removing dielectric rods from portions thereof, each of the plurality of splitting channel waveguides optically communicating with the main waveguide.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed.